Question: Solve for $x$ and $y$ using elimination. ${-2x-2y = -10}$ ${5x+3y = 21}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $2$ ${-10x-10y = -50}$ $10x+6y = 42$ Add the top and bottom equations together. $-4y = -8$ $\dfrac{-4y}{{-4}} = \dfrac{-8}{{-4}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {-2x-2y = -10}\thinspace$ to find $x$ ${-2x - 2}{(2)}{= -10}$ $-2x-4 = -10$ $-2x-4{+4} = -10{+4}$ $-2x = -6$ $\dfrac{-2x}{{-2}} = \dfrac{-6}{{-2}}$ ${x = 3}$ You can also plug ${y = 2}$ into $\thinspace {5x+3y = 21}\thinspace$ and get the same answer for $x$ : ${5x + 3}{(2)}{= 21}$ ${x = 3}$